Objective - To solve simple, one-step variable equations Lesson 2.3 Solving One-step Variable Equations 2:3 Solving One-Step Variable Equations Objective - To solve simple, one-step variable equations What is an equation? Equation - a balanced statement of equality between two quantities. 4 + 3 = 7 4 + 3 7 = fulcrum Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

4 + 3 7 = - 3 fulcrum Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4 = 7 fulcrum Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4 = 7 fulcrum Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4 = 7 fulcrum Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4 + 3 7 = - 3 - 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4 4 = Perform the same operation to both sides to keep the equation balanced. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

This property can be used to solve variable equations. x + 6 11 = -6 -6 x 5 = Algebraic Approach x + 6 = 11 -6 -6 x = 5 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve. 1) m + 2 = 10 4) m - 4 = 9 -2 -2 +4 +4 m = 8 m = 13 -2 -2 +4 +4 m = 8 m = 13 2) x - 4 = 6 5) 11 = x + 2 +4 +4 -2 -2 x = 10 9 = x 3) x + 7 = 3 6) 8 + y = -6 -7 -7 -8 -8 x = -4 y = -14 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Rules for Solving Equations 1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve. 1) -4 + x = 15 4) - 4 = m + 9 +4 +4 -9 -9 x = 19 -13 = m +4 +4 -9 -9 x = 19 -13 = m 2) 7 = x + 13 5) 9 + 7 = x -13 -13 16 = x -6 = x 3) -10 = 6 + x 6) y = 8 - 13 -6 -6 y = -5 -16 = x Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve. 1) 5x = 35 3) 9 = -3m 5 5 -3 -3 x = 7 -3 = m 2) 4) (-6) (-6) 5 5 -3 -3 x = 7 -3 = m 2) 4) (-6) (-6) -72 = x Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-4k = 14 -4 -4 Acceptable Answers All answers must be fully reduced! -4 -4 All answers must be fully reduced! There is nothing improper about an improper fraction! Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve. 1) 7x = 16 3) 9 = -m 7 7 (-1)9 = -m(-1) -9 = m 2) 4) (-4) (-4) 7 7 (-1)9 = -m(-1) -9 = m 2) 4) (-4) (-4) (-2) (-2) k = 16 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solving Equations Involving Fractions Long Way Short Way Easier to multiply by the reciprocal! Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve. 1) 3) 2) 4) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series